Q: Can I reform this to a tensor/matrix product? so I have the following vector matrix product:
$$v = A w$$
Now I have this $n$-times:
$$v^{(n)} = A^{(n)} w^{(n)} \quad \forall n$$
Is there any way to write this without $\forall$. Maybe somthing like this:
$$V = B W$$
where as the columns of $V$ are $v^{(n)}$ and the columns of $W$ are $w^{(n)}$.Then $B$ must be a 3 dimensional object. What is the correct name for it? Is it a rank 3 tensor? If yes, what tensor exactly?
Follow up: Lets say $A$ is column normalized. What is B called? Is there any smooth way to express this?
I hope the question makes sense. Thanks in advance,
Sascha
